Question

Giúp mk vs : B=1/2+1/2^2+1/2^3+...1/2^100

Answer 1

`text(B)=1/2+1/2^2+1/2^3+...+1/2^100`

`=>text(2B)=2.(1/2+1/2^2+1/2^3+...+1/2^100)`

`=>text(2B)=1+1/2+1/2^2+...+1/2^99`

`=>text(2B)-text(C)=(1+1/2+1/2^2+...+1/2^99)-(1/2+1/2^2+1/2^3+...+1/2^100)`

`=>text(B)=1-1/2^100`

Answer 2

\(B=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+....+\dfrac{1}{2^{100}}\)

\(2B=1+\dfrac{1}{2}+\dfrac{1}{2^2}+....+\dfrac{1}{2^{99}}\)

\(B=2B-B=1+\dfrac{1}{2}+....+\dfrac{1}{2^{99}}-\dfrac{1}{2}-\dfrac{1}{2^2}-....-\dfrac{1}{2^{100}}\Rightarrow B=1-\dfrac{1}{2^{100}}\)